An interesting question: "
how is the threshold crossing height determined? "
Several documents refer to, or infer wheel height as the basis of landing performance:
AC 91-79 para 6. g. Excessive Height Over the Runway Threshold – Threshold Crossing Height (TCH) Greater Than 50 ft (Excess TCH).
The certified landing distances furnished in the AFM are based on the landing gear being at a height of 50 ft over the runway threshold. For every 10 ft above the standard 50 ft threshold height, landing air distance will increase 200 ft. ( but the wheels will be much lower when following visual guidance; - see Min Eye Height below and # 9).
ICAO performance Manual
Air Distance. The length of the airborne distance from a point above the threshold to the point of main gear touchdown should be representative of a distance achievable in line operations following normal procedures and in line with the approach guidance provided.
(This suggest TCH referenced to wheel height.)
Airport information for visual guidance e.g. PAPI, publish a Min Eye height over the threshold. Note some runways have a second set of long body PAPI, suggesting that the increase is related to wheel referenced TCH.
References to PANS OPS / ICAO OPS (not verified) define a Reference Datum Height as
The height of the extended glide path or a nominal vertical path at the runway threshold.
According to ICAO Annex 10, the height of the ILS reference datum for ILS will be 15 m (50 ft). A tolerance of plus 3 m (10 ft) is permitted.
FAA Aeronautical Information Manual (unverified) defines Threshold Crossing Height :
The theoretical height above the runway threshold at which the aircraft’s glide slope antenna would be if the aircraft maintained the trajectory established by the mean ILS glide path.
The GS is increasingly irrelevant at lower altitudes due to angular sensitivity, parabolic effect, … Thence discussions on height difference; eye - ILS antenna - wheel, which are aircraft type dependent.
ILS GS is unlikely to agree with visual guidance with decreasing altitude.
Note, pilots more often refer to a fixed position for touchdown point, ground distance.
Performance calculations are based on air distance ( with corrections ) which gives a spread of touchdown position.
Also see, Theory, - (note ref to Reference Datum Height and assumptions) page 11, para 331
Reality, - page 30, fig 16; page 31, fig 17, et al, "
The influence of the threshold crossing height appears to have the strongest influence on the airborne distance."
http://www.tc.faa.gov/its/worldpac/techrpt/ar077.pdf
Re previous discussion defining touchdown:-
AC 91-97 Appx 1, para 2 I …
the TDZ is referred to as a point 500-3,000 ft beyond the runway threshold not to exceed the first one-third of the runway.
This reference is not used in landing distance performance calculations.